# Dimensions of Modulus of Rigidity

## Dimensional Formula of Modulus of Rigidity

The dimensional formula of modulus of rigidity is given by,

[ML-1 T-2]

Where,

• M = Mass
• L = Length
• T = Time

### Derivation

Modulus of Rigidity (μ) = shear stress × [shear strain]-1 . . . . (1)

Since, strain = ΔL/L = Dimensionless Quantity . . . . (2)

And, Stress = Force × [Area]-1 . . . . . (3)

The dimensional formula of,

Area = [MLT0] . . . . (4)

Force = [M1 LT-2] . . . . . (5)

On substituting equation (4) and (5) in equation (3) we get,

Stress = [M1 LT-2] × [MLT0]-1

∴ The dimensions of stress = [M1 L-1 T-2] . . . . (6)

On substituting equation (2) and (6) in equation (1) we get,

Modulus of Rigidity (μ) = shear stress × [shear strain]-1

Or, μ = [M1 L-1 T-2] × [M0 LT0]-1 = [ML-1 T-2].

Therefore, the Universal Gravitational Constant is dimensionally represented as [ML-1 T-2].